Nick Ritchie scored his first goal in his second game for Boston, and Jaroslav Halak made 31 saves to win his sixth straight start for the Bruins (40-13-12), who won for the first time in three games but are 12-3-0 in their past 15.
The Bruins lead the Tampa Bay Lightning, who lost 5-2 to the Chicago Blackhawks on Thursday, by seven points in the Atlantic.
Ritchie, who also had an assist, was traded to Boston by the Anaheim Ducks on Monday.
"It was good. It was nice to score, nice to win," Ritchie said. "It was a good night tonight."
WATCH: [All Stars vs. Bruins highlights]
Ben Bishop made 24 saves for the Stars (37-21-6), who had won their previous two games. They remained one point behind the Colorado Avalanche for second place in the Central Division.
"I thought we battled very hard," Dallas coach Rick Bowness said. "Clearly we can't give up four goals, and the two tap-ins at the bottom were a lot. But I thought we did a lot of really good things out there. That's the best team in the League, and we battled it for sixty minutes. I thought we had some good looks, we had a couple of breakdowns that gave them a couple easy goals. But we had a lot of good looks. We spent a lot more time in the offensive zone."
Jamie Benn scored on a power play at 17:38 to give Dallas a 1-0 lead. It was his 300th NHL goal.